To sum up: we have seen that of the three notions of 'partial interpretation' discussed, each is either unsuitable for Carnap's purposes (starting wi… - Hilary Putnam

It was Rudolf Carnap’s dream for the last three decades of his life to show that science proceeds by a formal syntactic method; today no one to my knowledge holds out any hope for that project.

In summary, then, the set theoretic 'needs' of physics are surprisingly similar to the set theoretic needs of pure logic. Both disciplines need some set theory to function at all. Both disciplines can 'live' - but live badly - on the meager diet of only predicative sets. Both can live extremely happily on the rich diet of impredicative sets. Insofar, then, as the indispensability of quantification over sets is any argument for their existence - and we will discuss why it is in the next section - we may say that it is a strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.

What I am saying, then, is that elements of what we call "language" or "mind" penetrate so deeply into what we call "reality" that the very project of representing ourselves as being "mappers" of something "language-independent" is fatally compromised from the very start. Like Relativism, but in a different way, Realism is an impossible attempt to view the world from Nowhere. In this situation it is a temptation to say, "So we make the world," or "our language makes up the world," or "our culture makes up the world"; but this is just another form of the same mistake. If we succumb, once again we view the world-the only world we know-as a product. One kind of philosopher views it as a product from a raw material: Unconceptualized Reality. The other views it as a creation ex nihilo. But the world isn't a product. It's just the world.